Question

The distinct linear functions that map [−1, 1] onto [0, 2] are
(a) $f\left(x\right)=x+1,g\left(x\right)=-x+1$
(b) $f\left(x\right)=x-1,g\left(x\right)=x+1$
(c) $f\left(x\right)=-x-1,g\left(x\right)=x-1$
(d) None of these

Answer 1

Let us substitute the end-points of the intervals in the given functions. Here, domain = [-1, 1] and range =[0, 2]
By substituting -1 or 1 in each option, we get:

Option (a):
$$\begin{gathered} f\left(-1\right)=-1+1=0\text{and}f\left(1\right)=1+1=2 \\ g\left(-1\right)=1+1=2\text{and}g\left(1\right)=-1+1=0 \end{gathered}$$
So, option (a) is correct.

Option (b):
$$\begin{gathered} f\left(-1\right)=-1-1=-2\text{and}f\left(1\right)=1-1=0 \\ g\left(-1\right)=-1+1=0\text{and}g\left(1\right)=1+1=2 \end{gathered}$$
Here, f(-1) gives -2$\notin \left[0,2\right]$
So, (b) is not correct.

Similarly, we can see that (c) is also not correct.